Checking the Numbers

To Subtract or Divide

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In this day and age, baseball players are defined by their statistical attributes much more than they were a few decades ago. That isn’t to say that stats rule all by any means, but rather that teams are starting to be built with more of an eye toward numbers than in the past or at least with an eye toward numbers that provide more information. We have witnessed the defensive revolution. This past offseason, not only did the Red Sox make a conscious effort to bring aboard the darlings of fielding metrics—Mike Cameron, Marco Scutaro, and Adrian Beltre—but teams shied away from the likes of Jermaine Dye, who averaged 33 home runs and a .279/.347/.528 line over the last four seasons, because his overall contributions were not in line with his asking price. And last offseason, the glut of hard-hitting but poor-fielding corner outfielders suffered financially; it’s hard to imagine players with skill sets similar to those of Adam Dunn and Bobby Abreu being offered so little even just a few years ago.

Simply put, with decisions hinging upon some of these numbers, it is imperative that users of the information not only utilize the appropriate toolkit but that they develop a solid understanding of why certain metrics are used. You don’t want to bring a knife to a gunfight, but on a more granular level, it also isn’t smart to bring a butter knife to a cleaver battle if such things exist. My favorite television show growing up was "The X-Files," so it should come as no surprise that my goal as an analyst has always been to spread the truth in whatever way possible. My goal today is to use a topic I recently wrote about as well as a couple of the ensuing comments to revisit what numbers we might use in a specific situation as well as why that specific number is used.

Over the last two weeks I have written about Cliff Lee’s strikeout-to-walk ratio, breaking down the metric itself, comparing his current rate to the single-season highs over the last few decades, and comparing his current rate to the rates of others through a similar point in the season. The articles found that nobody has ever had a K/BB ratio as high as his currently stands this deep into the season and that it would take a relative implosion—given where he is, a ratio of around 4.50 would be considered implosive—for Lee to not break the single-season K/BB record with a 150-inning minimum set by Bret Saberhagen at 11.00 in the strike-shortened 1994 campaign.

In the more recent piece, I took the 10 highest rates at a similar point in time and found their respective rates from that point forward. David Wells, at 14.50 on June 27, 2003, had the highest non-Lee rate, with Curt Schilling’s 13.64 on June 14, 2002, coming in second place. The dichotomous nature of how these two pitchers arrived at their rates tended to prove the shortcomings of the K/BB ratio in general, as Wells’ 14.50 consisted of 58 strikeouts and four walks, while Schilling whiffed 150 and issued just 11 free passes. Wells avoided walks but so did Schilling, and the latter punched out three times as many hitters. In other words, Wells posted the higher rate, but the inputs to Schilling’s rate added more value.

Value is the key, as the goal of most evaluators and analysts is to advise or discuss players in terms of the value they can add to a team. Wells issued a minuscule number of walks, but Schilling prevented many, many more hitters from doing harm to his team by preventing them from even making contact. Value can be tough to measure as well because some of the more telling numbers are not stable, meaning that they fluctuate from year to year. A pitcher with a 3.65 ERA in 2009 isn’t a lock to come anywhere near that mark in 2010, and so predictivity—a word I’ve wanted to use for a while but over which I was afraid to bypass the red squigglies—plays a major role in assessing value.

A player who has a solid season derived from numbers likely to repeat is more valuable than, say, Kyle Kendrick’s 2007 season, when he posted a sub-4.00 ERA but ended up with very poor peripherals. All of which brings us back to the Wells vs. Schilling conversation that surfaced in the comments of my articles. Several readers pointed out the very fact that Schilling produced a lower rate but added more value. It was also noted that the correlation of K/BB from one half of the season to another across the 10 pitchers tabled was irrelevant, while the correlation of the K-BB differential was quite high.

The differential simply subtracts walks from strikeouts, so even though Wells has the higher rate, his +54 paled in comparison to Schilling’s +139. The correlations were important because if the goal is to measure a specific aspect of performance—limiting walks and whiffing batters in this case—but one metric or rate proves more telling than another, we want to use that more informative rate. The K/BB ratio is more commonly used because of the familiarity associated with it, but if K-BB, or (K-BB)/PA is more predictive, then it is a better indicator of value because it offers more assistance in the decision-making department.

Is it a better indicator of value? If so, we would expect it to correlate with a common value-laden metric more than the K/BB ratio. To that end, I pooled every pitcher with 150 or more innings in a season from 2000-09 and ran a correlation measuring the relationship between (K-BB)/PA and ERA, while repeating the test for K/BB and K/UBB in order to see which bond proved stronger. Of the 960 pitchers from 2000-09 with 150 or more frames in a season, the r for K/UBB to ERA is -0.48, for K/BB to ERA is -0.49, and for (K-BB)/PA and ERA is -0.58. For those wondering whether or not these numbers are significant, the answer is yes because, in the context of baseball, correlation coefficients above 0.45 tend to matter more than they would in many other fields.

The inverse relationship suggests that as one goes up the other goes down—higher differential leads to a lower ERA and vice-versa—and the strikeout and walk differential clearly wins out in this regard. Backtracking to Wells and Schilling, the comments indicated that the split-half correlation comparisons between the differential and the ratio favored the former more than the latter, which is important because the differential has a stronger relationship with a common metric used to assess value.

With that in mind, comparisons of Lee’s strikeout and walk prowess at this juncture should involve finding whether or not anyone else, at a similar point in a given year, had a differential as vast if not more. Those hypothetical pitchers would then be used to potentially determine expected values for Lee over the remainder of the season. Currently, Lee has thrown 121 2/3 innings and has a +90 differential—97 punchouts and just seven walks. Using the same database techniques as last week—finding pitchers with similar numbers through a relatively equivalent point of the season—the tables below show the 10 highest K-BB differentials, as well as their differentials from that point forward:

OK, OK, so there isn’t much variety here, which just goes to show how rare it is for pitchers to exhibit this type of dominance in the comparison of strikeouts and walks. Additionally, the top 10 differentials and rates in the first table make Lee’s +90 and .189 look like puny, little girly-men. Though only three pitchers show up here, the aggregate rates do not fall that much over the second half, which is to be expected if we assume that there is a high correlation between first- and second-half differential. The numbers up to are better, for sure, but the decline from that point forward is nowhere near as significant as, say, David Wells falling from a 14.50 K/BB ratio to a 2.69 in his second half.

Anyway, the point here isn’t necessarily to showcase what might happen to Lee moving forward but rather to discuss, with the help of examples, why we use certain numbers and how we can choose the appropriate weapon from our arsenal. The goal is to determine value more often than not, and in order to do that, it is more helpful to find numbers that are likely to persist over the course of a season and into the next, and share a strong bond with numbers generally assigned to value. When discussing strikeout rates and walk rates, it is apparently more informative to use some form of the strikeout and walk differential, as it encompasses what the strikeout-to-walk ratio attempts to provide, while also accounting for the shortcomings.

Lee might still set the record for the single-season K/BB ratio with 150 or more innings, but over the last 40 years (1970-2009), the highest differential belongs to Randy Johnson’s 2001 season—a +303 differential. Color me skeptical Lee reaches that threshold. This does not take anything away from his fabulous season, but it lends itself to the idea that by obsessing over his ratio, we are actually asking the wrong questions. Rates and raw tallies have their places to be used, but hopefully this sheds light on when to use different types of rates and how to decide.

Eric Seidman is an author of Baseball Prospectus. Click here to see Eric's other articles.
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I think that sometimes people can obsess a little too much over the 'meaning' of a stat (i.e. is player a better than player b) or the predictive value of a stat. I subscribe to this site and am just as guilty as anyone of occasionally over-obsessing on one number.

I think the question we need to ask sometimes is 'what story does this stat tell'? Lee's K/BB this year tells the story of a guy that has had good control this season (but tells me nothing of how hard he has been hit, what runs he has given up, etc.) Johnson's +303 differential in 2001 tells the story of a guy that had a dominating performance in striking out batters (but tells me nothing of how hard he has been hit, what runs he has given up, etc.)

The problem is, no one stat can give me a complete story. Even a stat like WARP can't tell me everything. It can tell me how good someone is, but not 'why' someone was so good. The HOLY GRAIL of stats is to find one that can give you the complete story. I hope we never find it though...if one number can tell you everything, why watch the game?

I don't disagree with this article, but I think it's important to mention that just because a measurement is repeatable doesn't mean it's relevant. A pitcher could have the exact same K-BB/PA every year of his career so we could be sure that we really *understand* his K-BB/PA, but what exactly would that tell us about him? His ability to get strikeouts compared to his ability to prevent walks, two very specific aspects of pitching, neither one of which is its goal. In a sense, they're side effects, and they may or may not be related (in terms of skill).

If the goal of pitching is preventing runs (is it?), I'd want to know how Ks and BBs contribute to that goal. I would guess not equally, which makes any mathematical combination of K and BB without coefficients as spurious as OBP + SLG.

In other words, I think that certain *types* of pitchers will always have "good" K/BB numbers, but that those numbers don't tell us much about how good those pitchers are at preventing runs, only that they do two very well in two specific sub-tasks of pitching. Greg Maddux's best single-season K-BB/PA was .201 (in 1995), and yet his 1.63 ERA (262 ERA+) that year was better than Curt Schilling's 3.23 (142 ERA+) in 2002 when his K-BB/PA was .278. Which season was more valuable?

ERA and K-BB/PA are different stats, with different degrees of "repeatability," but repeatability can't be the sole determinant of a stat's relevance or value.

Alex, you're absolutely correct, but for a different topic, perhaps one I'll discuss in the future. Here it was showing that, if we are looking to evaluate the K and BB information for a pitcher, the differential has a stronger relationship with something we use to assess value than the K/BB ratio. Of course K and BB aren't the only inputs to value, but since peripherals are used so frequently to gauge performance, it is imperative to ask the appropriate question instead of using the wrong tool to get an answer.

When determining what tool to use in a situation, it depends on your goal. For most, if the idea is to use a K and BB-based metric, the goal is to use whatever is more likely to help determine value. These are subsets, for sure, but that doesn't mean we should blindly choose. It isn't the difference between choosing OBP over BA, but maybe equivalent to using ISO instead of Raw HR.

Why restict yourself to a single number? K and BB are two separate components of pitcher accomplishment. They can be inversely correlated (pitcher command) or positively correlated (pitching to contact). If you do a regression of ERA against BB/PA and K/PA as separate independent variables you will get a better fit (and more predictability) than you will by squeezing them into a ratio or difference.

Yes, agree that Differential (K-BB) is more predictive than K/BB. However, K/BB I believe is uses and will continue to be more prevalent as a metric because it is inherently scalable. We all know that pitchers like Halladay and Cliff Lee are studs, thus we really don't need a dozen different metrics that tell us what we already know.

The real "value add" in baseball is the predictivity of prospects/young MLB pitchers in terms of what they might become. K/BB (or better yet K% and BB% as % of Batters Faced) allow for easy compare points across pitchers with different innings totals, or to compare trends easily as a prospect jumps up the minor league levels.

This is exactly the kind of numerical article I value from BP -- it makes a simple but powerful point, and I will be able to apply it with some pretty easy computations instead of performing a regression analysis. The underlying statistical point is fairly basic (K-BB/PA having a higher correlation than K/BB with ERA is pretty straightforward), and the result makes considerable sense upon reflection.

With respect to Syd Finch, K-BB/PA is scalable, as opposed to raw K-BB, precisely because it accounts for the varying workloads of rookies under innings limits and 240 inning horses (keeping in mind that high durability is an extremely valuable trait even when coupled with league average peripherals).

And yeah, I have a renewed appreciation for Schilling's dominance. I have vivid memories of watching Schilling at the Vet in 1997 and 1998. The team was so bad and he was so good.

I think it is unfair in some sense that his mythology is based so much on what he accomplished in Boston, by which time he had clearly declined from great to good, precisely because Boston and baseball in general are consumed with the mythology of the Red Sox. Not to mention that his first season in Boston was by far his best, and that was (not entirely coincidentally) the apex of Red Sox mythology, Thermoplylae, Trafalgar and Little Round Top rolled into one.